*Unverified author*

R Software Module: /rwasp_exponentialsmoothing.wasp (opens new window with default values)

Title produced by software: Exponential Smoothing

Date of computation: Sun, 29 May 2011 11:49:58 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2011/May/29/t1306669571zl6vq66uv347m46.htm/, Retrieved Sun, 29 May 2011 13:46:14 +0200

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

KDGP2W102

Dataseries X:

» Textbox « » Textfile « » CSV «

505,7 55,7 735,7 575,9 545,8 905,8 765,8 945,7 15,7 645,7 155,9 416 825,8 725,9 925,9 556 116,1 876,3 336,2 186,1 286,1 26 915,8 405,7 965,7 395,6 425,8 545,6 65,6 445,6 895,5 175,4 715,4 865,5 57,4 145,4 315,3 635,4 5,2 515,2 515,1 955 955 634,9 205 275 425 84,9 534,7 4,8 704,7 684,7 884,6 994,6 294,7 524,7 914,5 564,4 984,5 934,4 514,6 474,5 784,4 504,5 824,4 414,6 964,7 64,6 244,7 344,7 34,7 685 425 484,8 785,1 704,9 245,4 285,6 218,8 706,1 856,2 456,6 606,8 527,3 657,8 948,2 486,6 238,9 289,4 969,5 589,5 189,7 639,8 9710,1 969,9 939,9 859,7 679,9 879,9 329,8 349,6 39,5 849,5 449,6 749,6 249,7 649,8 619,4 939 778,9

Output produced by software:

Summary of computational transaction Raw Input view raw input (R code) Raw Output view raw output of R engine Computing time 2 seconds R Server 'Herman Ole Andreas Wold' @ www.yougetit.org Estimated Parameters of Exponential Smoothing Parameter Value alpha 0.29089981285969 beta 0.129402100573134 gamma FALSE Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 3 735.7 -394.3 1130 4 575.9 -473.046568538926 1048.94656853893 5 545.8 -535.886020308952 1081.68602030895 6 905.8 -548.483614156879 1454.28361415688 7 765.8 -397.948971475575 1163.74897147557 8 945.7 -288.123744935826 1233.82374493583 9 15.7 -111.468894886917 127.168894886917 10 645.7 -251.952708950638 897.652708950638 11 155.9 -134.512542722383 290.412542722383 12 416 -182.786414262083 598.786414262083 13 825.8 -118.814239240618 944.614239240618 14 725.9 81.3173434025964 644.582656597404 15 925.9 218.433849937693 707.466150062307 16 556 400.474334378469 155.525665621531 17 116.1 427.809895101609 -311.709895101609 18 876.3 307.493008467076 568.806991532924 19 336.2 464.729947599733 -128.529947599733 20 186.1 414.273442800663 -228.173442800663 21 286.1 326.241520299882 -40.141520299882 22 26 291.396999737334 -265.396999737334 23 915.8 181.035350668403 734.764649331597 24 405.7 389.279318254505 16.4206817454948 25 965.7 389.175284593019 576.524715406981 26 395.6 573.707556372317 -178.107556372316 27 425.8 532.012930425985 -106.212930425985 28 545.6 507.23425939798 38.3657406020197 29 65.6 525.957700086072 -460.357700086072 30 445.6 382.27331874159 63.3266812584102 31 895.5 393.312435156616 502.187564843384 32 175.4 550.919970504003 -375.519970504003 33 715.4 439.066832234116 276.333167765884 34 865.5 527.239672276702 338.260327723298 35 57.4 646.16026092256 -588.76026092256 36 145.4 473.248003734599 -327.848003734599 37 315.3 363.89387557431 -48.5938755743102 38 635.4 333.945499501746 301.454500498254 39 5.2 417.173796403027 -411.973796403027 40 515.2 277.357986331911 237.842013668089 41 515.1 335.526571864868 179.573428135132 42 955 383.504527737267 571.495472262733 43 955 567.00536373342 387.994636266579 44 634.9 711.731141145494 -76.8311411454937 45 205 718.347028651095 -513.347028651095 46 275 578.656579926155 -303.656579926155 47 425 488.534484632216 -63.534484632216 48 84.9 465.872230341771 -380.972230341771 49 534.7 336.526439718177 198.173560281823 50 4.8 383.113907817676 -378.313907817676 51 704.7 247.760391178728 456.939608821272 52 684.7 372.58256531853 312.11743468147 53 884.6 467.025047316543 417.574952683457 54 994.6 607.863895069212 386.736104930788 55 294.7 754.289653094595 -459.589653094595 56 524.7 637.219051653267 -112.519051653267 57 914.5 616.875663288503 297.624336711497 58 564.4 727.046396692355 -162.646396692355 59 984.5 697.201953955125 287.298046044875 60 934.4 809.061039211828 125.338960788172 61 514.6 878.524397248303 -363.924397248303 62 474.5 791.96191286089 -317.461912860891 63 784.4 706.965122830915 77.4348771690849 64 504.5 739.758619827906 -235.258619827906 65 824.4 672.733785820247 151.666214179753 66 414.6 723.974492020653 -309.374492020653 67 964.7 629.45274457231 335.247255427689 68 64.6 735.07107096115 -670.471070961149 69 244.7 522.887550484607 -278.187550484607 70 344.7 414.34740570933 -69.6474057093298 71 34.7 363.849809467486 -329.149809467486 72 685 225.47281084047 459.52718915953 73 425 333.819807026754 91.1801929732464 74 484.8 338.447031230024 146.352968769976 75 785.1 364.63317724615 420.46682275385 76 704.9 486.38664439218 218.513355607821 77 245.4 557.617394219456 -312.217394219456 78 285.6 462.705854248112 -177.105854248112 79 218.8 400.431432002451 -181.631432002451 80 706.1 330.003359532417 376.096640467583 81 856.2 435.975702424141 420.224297575859 82 456.6 570.603295427711 -114.003295427711 83 606.8 545.532750212318 61.2672497876823 84 527.3 573.754659753437 -46.4546597534367 85 657.8 568.891591035103 88.9084089648967 86 948.2 606.752397078215 341.447602921785 87 486.6 730.929935493442 -244.329935493442 88 238.9 675.507574399983 -436.607574399983 89 289.4 547.716444757507 -258.316444757507 90 969.5 462.066353332924 507.433646667076 91 589.5 618.274168730914 -28.7741687309144 92 189.7 617.416083594395 -427.716083594395 93 639.8 484.405333513077 155.394666486923 94 9710.1 526.8709202162 9183.2290797838 95 969.9 3541.21657067186 -2571.31657067186 96 939.9 3039.37490104804 -2099.47490104804 97 859.7 2595.76125277685 -1736.06125277685 98 679.9 2192.51393172237 -1512.61393172237 99 879.9 1797.32799746341 -917.427997463409 100 329.8 1540.74675501591 -1210.94675501591 101 349.6 1153.19723550532 -803.597235505315 102 39.5 853.895766611914 -814.395766611914 103 849.5 520.796669051269 328.703330948731 104 449.6 532.598279934586 -82.9982799345859 105 749.6 421.511661118665 328.088338881335 106 249.7 442.360307493709 -192.660307493709 107 649.8 304.47094911205 345.32905088795 108 619.4 336.081832042037 283.318167957963 109 939 360.318719799598 578.681280200402 110 778.9 492.260008170372 286.639991829628 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 111 550.036543045553 -1559.58557916765 2659.65866525876 112 524.429557939392 -1696.13228305648 2744.99139893526 113 498.822572833231 -1852.27772252172 2849.92286818818 114 473.21558772707 -2027.47458688231 2973.90576233645 115 447.608602620909 -2220.8823313827 3116.09953662452 116 422.001617514748 -2431.49849089524 3275.50172592474 117 396.394632408587 -2658.26100847144 3451.05027328861 118 370.787647302426 -2900.11914368315 3641.694438288 119 345.180662196265 -3156.07711823423 3846.43844262676 120 319.573677090104 -3425.21713642029 4064.3644906005 121 293.966691983942 -3706.70831788113 4294.64170184902 122 268.359706877781 -3999.80683876093 4536.52625251649

Charts produced by software:

http://www.freestatistics.org/blog/date/2011/May/29/t1306669571zl6vq66uv347m46/16aoi1306669796.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/29/t1306669571zl6vq66uv347m46/16aoi1306669796.ps (open in new window) http://www.freestatistics.org/blog/date/2011/May/29/t1306669571zl6vq66uv347m46/2hg0u1306669796.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/29/t1306669571zl6vq66uv347m46/2hg0u1306669796.ps (open in new window) http://www.freestatistics.org/blog/date/2011/May/29/t1306669571zl6vq66uv347m46/3rky81306669796.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/29/t1306669571zl6vq66uv347m46/3rky81306669796.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Double ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Double ; par3 = additive ;

R code (references can be found in the software module):

par1 <- as.numeric(par1) if (par2 == 'Single') K <- 1 if (par2 == 'Double') K <- 2 if (par2 == 'Triple') K <- par1 nx <- length(x) nxmK <- nx - K x <- ts(x, frequency = par1) if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F) if (par2 == 'Double') fit <- HoltWinters(x, gamma=F) if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3) fit myresid <- x - fit$fitted[,'xhat'] bitmap(file='test1.png') op <- par(mfrow=c(2,1)) plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing') plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors') par(op) dev.off() bitmap(file='test2.png') p <- predict(fit, par1, prediction.interval=TRUE) np <- length(p[,1]) plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing') dev.off() bitmap(file='test3.png') op <- par(mfrow = c(2,2)) acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF') spectrum(myresid,main='Residals Periodogram') cpgram(myresid,main='Residal Cumulative Periodogram') qqnorm(myresid,main='Residual Normal QQ Plot') qqline(myresid) par(op) dev.off() load(file='createtable') a<-table.start() a<-table.row.start(a) a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Parameter',header=TRUE) a<-table.element(a,'Value',header=TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'alpha',header=TRUE) a<-table.element(a,fit$alpha) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'beta',header=TRUE) a<-table.element(a,fit$beta) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'gamma',header=TRUE) a<-table.element(a,fit$gamma) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'t',header=TRUE) a<-table.element(a,'Observed',header=TRUE) a<-table.element(a,'Fitted',header=TRUE) a<-table.element(a,'Residuals',header=TRUE) a<-table.row.end(a) for (i in 1:nxmK) { a<-table.row.start(a) a<-table.element(a,i+K,header=TRUE) a<-table.element(a,x[i+K]) a<-table.element(a,fit$fitted[i,'xhat']) a<-table.element(a,myresid[i]) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable1.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'t',header=TRUE) a<-table.element(a,'Forecast',header=TRUE) a<-table.element(a,'95% Lower Bound',header=TRUE) a<-table.element(a,'95% Upper Bound',header=TRUE) a<-table.row.end(a) for (i in 1:np) { a<-table.row.start(a) a<-table.element(a,nx+i,header=TRUE) a<-table.element(a,p[i,'fit']) a<-table.element(a,p[i,'lwr']) a<-table.element(a,p[i,'upr']) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable2.tab')

Copyright

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa

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